Number Base System Polished

-- functions
function splitChars(str)
    str = tostring(str)

    return str:split''
end

function flipTable(t)
    local t2 = {}

    for i, v in next, t do
        t2[v] = i
    end

    return t2
end

function arrayToCharDict(arr)
    local dict = {}

    for i, v in next, arr do
        dict[i - 1] = v
    end

    return dict
end

function stringToCharDict(str)
    return arrayToCharDict(splitChars(str))
end

--  base system
function factNumToStrFromBase(charsDict)
    local base = #charsDict + 1

    return function(num)
        local res = ''

        local iterations = 1 + math.max(0, math.floor( math.log(num, base)))

        for i = iterations, 1, -1  do -- going down number places
            local factor = base ^ (i - 1)

            local index = base - 1

            for largestDigit = base, 0, -1 do -- going down the base to 1
                local num2 = factor * largestDigit

                if num - num2 < 0 then continue end

                index = largestDigit
                num -= num2

                break
            end
            res ..= charsDict[index]
        end

        return res
    end
end

function factStrToNumFromBase(charsDict)
    local base = #charsDict + 1
    local flippedCharacters = flipTable(charsDict)

    return function(str)
        local res = 0

        for index = 1, #str do -- iterate each letter
            local letter = str:sub(index, index)

            local num = flippedCharacters[letter] * base ^ (#str - index)

            res += num
        end

        return res
    end
end

local binary = stringToCharDict'01'

local numToStr_Bin = factNumToStrFromBase(binary)
local strToNum_Bin = factStrToNumFromBase(binary)


for n = 1, 10 do
    local s = numToStr_Bin(n)

    print(n, s, strToNum_Bin(s))
end